Pith Number

pith:RDOYYJ5J

pith:2026:RDOYYJ5JL7J4TG6O3HDHZSHGAH

not attested not anchored not stored refs pending

Critical exponents for planar random-cluster model with cluster-weight $q=4$

Dmitry Krachun, Fran\c{c}ois Jacopin, Hong-Bin Chen, Hugo Duminil-Copin, Ioan Manolescu, Jiaming Xia, Tiancheng He

arxiv:2605.30030 v1 · 2026-05-28 · math.PR · cond-mat.stat-mech · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RDOYYJ5JL7J4TG6O3HDHZSHGAH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-29T02:06:07.732288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88dd8c27a95fd3c99bced9c67cc8e601ee191dc52c745a50eb590347f1a962e9

Aliases

arxiv: 2605.30030 · arxiv_version: 2605.30030v1 · doi: 10.48550/arxiv.2605.30030 · pith_short_12: RDOYYJ5JL7J4 · pith_short_16: RDOYYJ5JL7J4TG6O · pith_short_8: RDOYYJ5J

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RDOYYJ5JL7J4TG6O3HDHZSHGAH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 88dd8c27a95fd3c99bced9c67cc8e601ee191dc52c745a50eb590347f1a962e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e0fe9e73776886ce89d355c0954ae4e4d809e3eba77eafe188468d3268d4d50",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-28T14:53:14Z",
    "title_canon_sha256": "17bd601ba1dfe0ab6c4bbf6aeb0b05adeb6558351e8927b69d439cd89f9879e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.30030",
    "kind": "arxiv",
    "version": 1
  }
}